The generator coordinate method applied to variational perturbation theory. Multipole polarizabilities, spectral sums, and dispersion coefficients for helium

It is shown that a suitable variant of the generator coordinate method can be used for accurate variational perturbation theory calculations. The test problems chosen are calculations of the dipole, quadrupole, and octupole polarizabilities, spectral sums, two-body dispersion coefficients, and nonadditive three-body dispersion coefficients for the ground state of atomic helium. An accurate explicitly correlated wave function for the unperturbed problem is utilized along with explicitly correlated basis functions for the pseudospectra. The dipole results are in excellent agreement with previous high accuracy calculations. The quadrupole and octupole results are expected to be the most accurate ones currently available. Estimates of some hexadecapole properties are made.